What is the frequency of the wave?

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The discussion revolves around calculating the frequency of a sound wave traveling at 345 m/s through air, with specific displacements of air molecules at given positions. The maximum displacement (sm) is identified as 6.30 nm, while the displacement at a nearby position is 2.40 nm. The equation s = sm cos(kx - ωt + φ) is used to relate displacement to wave parameters, but confusion arises regarding the use of the inverse cosine function to determine the phase. The key challenge is finding the value of the phase angle without a clear method presented. The thread emphasizes the importance of understanding wave properties and mathematical relationships in wave mechanics.
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A sound wave of the form s = sm cos(kx - ωt + φ) travels at 345 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.00 m is at its maximum positive displacement of 6.30 nm and air molecule B at x = 2.09 m is at a positive displacement of 2.40 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?
Here is what I've gotten so far.
s=6.30 nm at 2m
s=240nm at 2.09
since s is max at 2m, the sm=6.40nm

s=smcos(kx-wt+phi)
kx-wt + phi=acos(s/sm)

I have everything I need but, how do I find out what the value of a is?
 
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There is no a, acos stands for arccos(y), the inverse cosine function.
 
Thank you!
 
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